Question

Suppose Stocks A, B and C are the only three component stocks in a benchmark index. The number of shares outstanding of Stocks A, B and C are 371,000 shares, 312,000 shares, and 234,000 shares, respectively. The prices of Stocks A, B and C for Days 1, 2, 3 and 4 are given in the table below:

	Stock A	Stock B	Stock C
Day 1	30.37	41.70	81.85
Day 2	31.03	40.61	78.65
Day 3	32.05	42.03	79.28
Day 4	33.49	44.65	79.92

If the benchmark value-weighted index was 1508.13 on Day 1, the benchmark value-weighted index on Day 4 was ( )? (Note: Answer must be correct to 2 decimal places, but you may leave your answer with more than 2 decimal places.)

Answer 1

Answer: Value weighted Index is calculated by Multiplying the price of the individual stocks with their number of shares outstanding and dividing by an arbitrary number which is decided in the starting of the index.

Here we have been given Share price, their outstanding volumes and Value weighted index on Day 1

Lets calculate the value of the divisor through this information first

Value Weighted Index on Day 1 = Share price A (Day 1) * Volume of Shares A + Share price B(Day 1) * Volume of B + Share Price C (Day 1)* Volume C / Divisor

1508.13 = 30.37 * 371000 + 41.7*312000 + 81.85*234000/Divisor

On Solving this

Divisor = 11267270 + 13010400 + 19152900 / (1508.13)

Divisor = 43430570/1508.13

Divisor = 28797.63

Now we will use this value to calculate the value weighted index on Day 4

Value weighted index on day 4 = 33.49 *371000 + 44.65 *312000 +79.92*234000 /(28797.63)

Value weighted index on day 4 = 12424790 + 13930800 + 18701280 / (28797.63)

Value weighted Index on Day 4 = 45056870 /(28797.63)

Value weighted Index on Day 4 = 1564.603